Fractal analysis, which provides a means for quantifying the complexity or degree of irregularity of any object or pattern, is a widely used analytical tool in a variety of research areas including physics, signal and image processing, acoustics, geophysics, biology, electrochemistry, and even sociology. In the field of image processing in particular, fractal analysis is used for various tasks, such as denoising, segmentation, estimation, compression, edge detection, classification, and synthesis, Computation of different fractal quantities, such as fractal dimensions, Holder exponents or multifractal spectra, provide improved indices for the analysis of irregular, but otherwise self-similar (scale-invariant) objects, also referred to as fractal objects, which cannot be represented with conventional Euclidean geometries.
Global measures of regularity are commonly used for applications such as classification or monitoring of fractal objects. The most well known measures of global regularity are fractal dimension estimates, defined either as regularization dimension, classical box-dimension or Hausdorff dimension. Fractal dimension D has become a widely accepted parameter for quantifying the complexity of feature details present in an object, and there are many methods and algorithms available for fractal dimension estimation of such geometries.
The fractal concept can also be extended to complex time-varying signals or processes that lack a single time scale in analogy to fractal geometries that lack a single length scale. Examples of time-varying signals include brain electrical signals, cardiac signals, output from chemical or electrical sensors in response to sensed parameters, radar signal, etc. Such time-varying signals generate irregular fluctuations across multiple time scales, and can be considered as fractal time-series. As similar to fractal objects, fractal time-series can be characterized by their fractal dimension D.
The use of fractal techniques to analyze temporal events has been previously demonstrated through conversion of the temporal signal into spatial patterns, as disclosed in U.S. Pat. No. 6,422,998 to Vo-Dinh et al. The disclosed method of Fractal Analysis with Space-Time (FAST) coordinate conversion is based on the concept that, when the temporal signal of a process is converted into a spatial pattern, the element of this spatial pattern can be characterized and analyzed by fractal geometry. However, this technique does not involve modification or restoration of the signal in the spatial domain based on the fractal dimension estimate, and reconstruction of the modified signal.
The present invention involves a novel approach of using fractal dimensions to characterize and modify time-varying signals, by coupling fractal dimension analysis with signal decomposition. The proposed method can be used for various signal processing tasks, such as denoising, separation, classification, monitoring, edge detection etc.
Signal decomposition techniques are commonly used to correct or remove signal contaminates. These techniques are based on the “unmixing” of the input signal into some number of underlying components using a source separation algorithm, followed by “remixing” only those components that would result in a “clean” signal by nullifying the weight of unwanted components. There are various algorithms available for signal decomposition based on wavelet transform, Fast Fourier Transform, Independent Component Analysis (ICA), etc. The components that generate artifacts are identified and set to zero in the transform domain, and the “clean” signal is reconstructed using an inverse transform. Such a technique using wavelet transform is disclosed in U.S. Patent Publication No. 2007/0032737 A1 (application Ser. No. 11/195,001), incorporated herein by reference in its entirety.
The recognition and cancellation of unwanted components after the signal decomposition is, however, a complicated and tedious task, and is often performed by a human expert. There is currently no known method of automatic characterization and modification of signals based on their transform coefficients. The current invention presents a technique for automatic, real-time processing of signals by combining the signal transform method with fractal dimension analysis for selective processing of unwanted coefficients.